An oscillator circuit of this kind is known, for example, from U.S. Pat. No. 6,281,758, in which an LC oscillator with two varactors is described. In this case, the LC oscillator is fed with a constant current which is supplied by a constant current source formed by a current mirror. Despite the constant current source, the frequency of the LC oscillator is strongly affected by the noise, which is produced in particular in the case of an integrated circuit by surrounding circuit components. In order to reduce the sensitivity of the LC oscillator to noise, the oscillator described in U.S. Pat. No. 6,281,758 is designed differentially. Disadvantageously, this means high cost of the circuit and a restriction in the circuit options, which may be used in the construction of an LC oscillator.